Mathmetics
ISBT Mathmetics for all banking PO,Clerk,IBPS PO,Railway,SSC,IAS,OAS Exams
Q1. 

1)  53/10 days  2)  67/10 days 
3)  63/10 days  4)  73/10 days 
5)  None of these 
Answer : 63/10 days
Explanation : A,B and C altogether work for 3 days = 3 (1/12+1/18+1/24) = 13/24 parts
Explanation : A,B and C altogether work for 3 days = 3 (1/12+1/18+1/24) = 13/24 parts
So, remaining (113/24) = 11/24 parts
B and C can do in 1 day (1/12+1/18) = 5/36 parts
Now, B & C can do this in (11/24 )/(5/36) = 33/10 days = 33/10 days
So, overall time taken to complete this workpiece = 63/10 days
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Q2.  A is 25% more efficient than B and 50% more efficient than C. A and B together can complete a work in 20 days. How many days the same work can be completed by B and C if both work in alternate days and B starts the work first ? 
1)  48 days  2)  49 days 
3)  50 days  4)  51 days 
5)  None of these 
Answer : 49 days
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Q3. 

1)  8 days  2)  10 days 
3)  12 days  4)  14 days 
5)  None of these 
Answer : 14 days
Explanation : Let, Bikas takes x days to finish the work . So, Alok would take (x +8) days to finish the same work.
Explanation : Let, Bikas takes x days to finish the work . So, Alok would take (x +8) days to finish the same work.
Given, Alok finishes 75% and Bikas finishes 25% work respectively.
So, (x+8)3/4 = (x/4)+9
or (3x+24)/4 = (x+36)/4
or 2x = 12
or x = 6
Therefore, Alok would finishes the work (6+8) = 14 days alone.
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Q4.  A fort has provisions for 250 soldiers for 35 days. After 5 days a reinforcements of 25 soldiers were arrived. Again after 10 days, 25 soldiers left the fort. How long will the remaining provisions lasting ? 
1)  12  2)  16 
3)  18  4)  19 
5)  None of these 
Answer : 19
Explanation :
Explanation :
Short Cut Methods:
ND (No. of days) = N_{1}D_{1} + N_{2}D_{2} = total amount of food after 5 days.
or ( 250 X 30) = ( 250 + 25) X 10 + 250 X x
or x = 19 days .
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Q5.  Seven men and four boys can complete a work in 6 days. A man completes the double work than a boy. In how many days will 5 men and 4 boys complete the work ? 
1)  4  2)  5 
3)  6  4)  8 
5)  None of these 
Answer : None of these
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Q6. 

1)  9 days  2)  11 days 
3)  14 days  4)  12 days 
5)  None of these 
Answer : 12 days
Explanation :
Explanation :
3 men = 8 boys
2 m = (8/3)x2 = 16/3 boys.
(2 men + 6 boys) = (16/2)+6 boys = 34/3boys
8 boys can complete the work in 17 days
or 34/3boys boys can complete the work in x days
or (34/3) : 8 = 17 : x
or x =(17x8x3)/34 = 12 days
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Q7.  10 man can finish a piece of work in 15 days. 8 women can finish the same work in 25 days. Only 10 women started working and in a few days completed a certain amount of work. After that 3 men joined them. The remaining work was completed by 10 women and 3 men together in 5 days . After how many did 3 men join with 10 women ? 
1)  11  2)  13 
3)  15  4)  10 
5)  None of these 
Answer : 13
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Q8.  16 men can complete a piece of work in 8 days. 20 women take 16 days to complete the same piece of work. 12 men and 10 women work together for 6 days. How many more days would 10 women alone require to complete the remaining piece of work ? 
1)  6 days  2)  8 days 
3)  10 days  4)  12 days 
5)  None of these 
Answer : 8 days
Explanation : Given,16 men can complete a piece of work in 8 days while 20 women take 16 days to complete the same piece of work.
Explanation : Given,16 men can complete a piece of work in 8 days while 20 women take 16 days to complete the same piece of work.
The ratio of the capacity of doing work i.e. men to women = (20 x 16 ) : (16 x 8) = 5:2
So, 1 man = 2.5 women
Now, 12m + 10w = (12 x 2.5) = 40w
Given, 20 women take 16 days to complete the same piece of work.
Given, 20 women take 16 days to complete the same piece of work.
1 woman can do it in = 16 x 20 = 320 days i.e. 1/320 parts in 1 day.
40 women can do in 6 days = (1/320) x 40 x 6 = 6/8 = 3/4 parts
Therefore, remaining 13/4=1/4 part of the work done by only 10 women in =
Applying Chain Rule:
M_{1} x D_{1} x W_{2} = M_{2} x D_{2} x W_{1}
or 20w x16 x 1/4 = 10w x D_{2} x 1
or D_{2} = 8 days
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Q9.  A,B,C can do a work in 36,54 and 72 days respectively.They started work together but A and B left the work 8 and 12 days before completion of the work respectively. Find the total number of days which the work has been completed ? 
1)  15  2)  18 
3)  24  4)  30 
5)  None of these 
Answer : 24
Explanation : Let,the total numbers of days requires to finish the job is x days.
Explanation : Let,the total numbers of days requires to finish the job is x days.
So, A works for ( x8) days and B works for (x12) and C works for x days.
Therefore,
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Q10.  A and B can do a work together in 12 days while B and C together can do the same work in 15 days. If A is twice good work as C then, in how many days C can alone do the same work ? 
1)  30 days  2)  36 days 
3)  45 days  4)  60 days 
5)  None of these 
Answer : 60 days
Explanation : Given, A+B can do the work in 1day =1/12 parts  (I) :
Explanation : Given, A+B can do the work in 1day =1/12 parts  (I) :
B+C in 1day =1/15 parts  (II)
and also given A = 2C.
So, putting the value in equation I, we get 2C+B = 12 .
Then, deducting equation II from equation I , we get, 1/12  1/15= c =1/60 i.e 60 days.
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